1. Field of the Invention
The present invention relates generally to characteristic compensation of an analog part in an orthogonal converter (a real-to-complex mixer) or a complex mixer, and in particular, to a frequency converter for canceling an image signal present in mixer output.
2. Description of the Related Art
In an orthogonal converter or a complex mixer realized by an analog circuit, if a real part is I and an imaginary part is Q, the amplitudes of I and Q are different and the phase difference between I and Q is not exactly 90°. Therefore, an image signal, which should not appear under an ideal circumstances, is observed in the complex conjugate of the signal frequency output from the mixer.
The image signal is generated in the band of the target signal, causing interference with the target (or wanted) signal in the receiver.
An image signal generated simply due to the I−Q amplitude difference is described by                                                                         f                ⁡                                  (                                      ω                    ⁢                                                                                   ⁢                    t                                    )                                            =                            ⁢                                                cos                  ⁡                                      (                                          ω                      ⁢                                                                                           ⁢                      t                                        )                                                  ⁢                                  (                                                            A                      ⁢                                                                                           ⁢                                              cos                        ⁡                                                  (                                                                                    ω                              c                                                        ⁢                            t                                                    )                                                                                      -                                                                  j                        ⁡                                                  (                                                      A                            -                            d                                                    )                                                                    ⁢                                              sin                        ⁡                                                  (                                                                                    ω                              c                                                        ⁢                            t                                                    )                                                                                                      )                                                                                                        =                            ⁢                                                cos                  ⁡                                      (                                          ω                      ⁢                                                                                           ⁢                      t                                        )                                                  ⁢                                  (                                                            A                      ⁢                                                                                           ⁢                                              ⅇ                                                                              -                            1                                                    ⁢                          j                          ⁢                                                                                                           ⁢                                                      ϖ                            c                                                    ⁢                          t                                                                                      +                                          j                      ⁢                                                                                           ⁢                      d                      ⁢                                                                                           ⁢                      sin                      ⁢                                                                                           ⁢                                              (                                                                              ω                            c                                                    ⁢                          t                                                )                                                                              )                                                                                                        =                            ⁢                                                                    A                    2                                    ⁢                                      (                                                                  ⅇ                                                  j                          ⁡                                                      (                                                                                          ω                                ⁢                                                                                                                                   ⁢                                t                                                            -                                                                                                ω                                  c                                                                ⁢                                t                                                                                      )                                                                                              +                                              ⅇ                                                  -                                                      j                            ⁡                                                          (                                                                                                ω                                  ⁢                                                                                                                                           ⁢                                  t                                                                +                                                                                                      ω                                    c                                                                    ⁢                                  t                                                                                            )                                                                                                                                            )                                                  +                                                                                                      ⁢                                                d                  4                                ⁢                                  (                                                            ⅇ                                              j                        ⁡                                                  (                                                                                    ω                              ⁢                                                                                                                           ⁢                              t                                                        +                                                                                          ω                                c                                                            ⁢                              t                                                                                )                                                                                      -                                          ⅇ                                              j                        ⁡                                                  (                                                                                    ω                              ⁢                                                                                                                           ⁢                              t                                                        -                                                                                          ω                                c                                                            ⁢                              t                                                                                )                                                                                      +                                          ⅇ                                              -                                                  j                          ⁡                                                      (                                                                                          ω                                ⁢                                                                                                                                   ⁢                                t                                                            -                                                                                                ω                                  c                                                                ⁢                                t                                                                                      )                                                                                                                -                                          ⅇ                                              -                                                  j                          ⁡                                                      (                                                                                          ω                                ⁢                                                                                                                                   ⁢                                t                                                            +                                                                                                ω                                  c                                                                ⁢                                t                                                                                      )                                                                                                                                )                                                                                                        =                            ⁢                                                                    1                    2                                    ⁢                                      (                                          A                      -                                              d                        2                                                              )                                    ⁢                                      (                                                                  ⅇ                                                  j                          ⁡                                                      (                                                                                          ω                                ⁢                                                                                                                                   ⁢                                t                                                            -                                                                                                ω                                  c                                                                ⁢                                t                                                                                      )                                                                                              +                                              ⅇ                                                  -                                                      j                            ⁡                                                          (                                                                                                ω                                  ⁢                                                                                                                                           ⁢                                  t                                                                +                                                                                                      ω                                    c                                                                    ⁢                                  t                                                                                            )                                                                                                                                            )                                                  +                                                                                                      ⁢                                                d                  4                                ⁢                                  (                                                            ⅇ                                              -                                                  j                          ⁡                                                      (                                                                                          ω                                ⁢                                                                                                                                   ⁢                                t                                                            -                                                                                                ω                                  c                                                                ⁢                                t                                                                                      )                                                                                                                -                                          ⅇ                                              j                        ⁡                                                  (                                                                                    ω                              ⁢                                                                                                                           ⁢                              t                                                        +                                                                                          ω                                c                                                            ⁢                              t                                                                                )                                                                                                      )                                                                                        (        1        )            where d=A−B, cos(ωt) is mixer input, lo(ωct) is a local signal, A and B are amplitudes of the local signal, ωc indicates a carrier frequency of the local system and f(ωt)=cos(ωt)lo(ωct)=cos(ωt)A cos(ωct)−jB sin(ωct)) is mixer output.
In equation (1), the first term in the final formulation of the equation represents the target signal, the second term represents the image signal generated due to non-orthogonality of the mixer, and the image frequency is the complex conjugate of the frequency of the target signal in the first term.
The image signal is not generated when perfect orthogonality is established between I and Q, that is, when the second term in Eq. 1 is zero. Thus, some methods of compensating the I−Q orthogonality have been suggested. For example, mixers having the function of adjusting the I−Q orthogonality are disclosed in Japanese Patent Laid-Open No. Hei 7-30463, Japanese Patent Laid-Open No. Hei 8- 125447 (Publication No. 2988277), and Japanese Patent Laid-Open No. 2000-22449. Methods of compensating I−Q characteristics after sampling using an analog-to-digital converter (ADC) are disclosed in Japanese Patent Laid-Open No. Hei 6-188928 and Japanese Patent Laid-Open No. Hei 10-313261.
Image signal cancellation is not perfect by adjustment of I−Q characteristics in the nature of an analog part and adjusted characteristics vary with environmental changes including time and temperature. Thus, compensation is adapted by monitoring mixer output or compensated output, as disclosed in Japanese Patent Laid-Open No. Hei 6-188928, Japanese Patent Laid-Open No. Hei 8-125447 (Publication No. 2988277), Japanese Patent Laid-Open No. Hei 10-56484, Japanese Patent Laid-Open No. Hei 10-313261, Japanese Patent Laid-Open No. 2000-13147, and Japanese Patent Laid-Open No. 2000-22449.
The technology disclosed in Japanese Patent Laid-Open No. Hei 10-56484 will be described below with reference to FIGS. 7A and 7B, by way of example. Referring to FIG. 7A, an orthogonality and amplitude error compensation circuit is placed at the output of an orthogonal converter. The orthogonality and amplitude error compensation circuit calculates the equations of Yi=h3×Xi and Yq=h1×Xq+h2×Xi with two components Xi and Xq received from the orthogonal converter and coefficients h1 and h2 adaptively updated in the formulas shown in FIG. 7B, and achieves orthogonality and an amplitude error-compensated two components Yi and Yq.
However, the above methods basically compensate I−Q orthogonality, neglecting I−Q frequency characteristics. The image suppression varies with frequency within a channel band in recent wireless communication systems requiring wide-band orthogonality such as CDMA (Code Division Multiple Access). Thus, though improved constellation effects reduction in BER (Bit Error Rate), there is a limit on BER reduction by image frequency disturbance. In the case of digital signal processing, even if the signal level of an image frequency is much higher than that of a target signal frequency, it is necessary to detect a fine phase difference or amplitude difference. Therefore, a wide dynamic range for signal processing is required.
With these problems overcome, both phase and amplitude should be adjusted. When an adaptive algorithm for digital signal processing is used, a simple algorithm like LMS (Least Mean Squares) is not applicable.
An image signal canceling method disclosed in Japanese Patent Laid-Open No. Hei 6-22292 also has limitations in complying with rapid changes in an input signal due to paging, for example and problems in stability, because it relies on feedback.